The basic idea Valentini proposes is that we could be living in a deterministic cosmos, but we are somehow trapped in a region of phase space where quantum indeterminism reigns. In the our present epoch region there are hidden variables but they cannot be observed, not even indirectly, so they have no observable consequences, and so Bell’s Theorem and Kochen-Specker and the rest of the “no-go” theorems associated with quantum logic hold true. Fine, you say, then really you’re saying there effectively are no Hidden Variables (HV) theories that describe our reality? No, says Valetini. The Hidden Variables would be observable if the universe was in a different state, the other phase. How might this happen? And what are the consequences? And is this even remotely plausible?

Last question first: Valentini thinks it is testable using the microwave cosmic background radiation. Which I am highly sceptical about. But more on this later.

The idea of non-equilibrium Hidden Variable theory in cosmology. The early universe violates the Born Rule and hidden variables are not hidden. But the violent history of the universe has erased all pilot wave details and so now we only see non-local hidden variables which is no different from conventional QM. (Apologies for low res image, it was a screenshot.)

How Does it Work?

How it might have happened is that the universe as a whole might have two (at least, maybe more) sorts of regimes, one of which is highly non-equilibrium, extremely low entropy. In this region or phase the Hidden Variables would be apparent and Bell’s Theorems would be violated. In the other type of phase the universe is in equilibrium, high entropy, and Hidden Variables cannot be detected and Bell’s Theorem’s remain true (for QM). Valentini claims early during the Big Bang the universe may have been in the non-equilibrium phase, and so some remnants of this HV physics should exist in the primordial CMB radiation. But you cannot just say this and get hidden variables to be unhidden. There has to be some plausible mechanism behind the phase transition or the “relaxation” process as Valentini describes it.

The idea being that the truly fundamental physics of our universe is not fully observable because the universe has relaxed from non-equilibrium to equilibrium. The statistics in the equilibrium phase get all messed up and HV’s cannot be seen. (You understand that in the hypothetical non-equilibrium phase the HV’s are no longer hidden, they’d be manifest ordinary variables.)

Further Details from de Broglie-Bohm Pilot Wave Theory

Perhaps the most respectable HV theory is the (more or less original) de Broglie-Bohm pilot wave theory. It treats Schrödinger’s wave function as a real potential in a configuration space which somehow guides particles along deterministic trajectories. Sometimes people postulate Schrödinger time evolution plus an additional pilot wave potential. (I’m a bit vague about it since it’s a long time since I read any pilot wave theory.) But to explain all manner of EPR experiments you have to go to extremes and imagine this putative pilot Wave as really an all-pervading information storage device. It has to guide not only trajectories but also orientations of spin and units of electric charge and so forth, basically any quantity that can get entangled between relativistically isolated systems.

This seems like unnecessary ontology to me. Be that as it may, the Valentini proposal is cute and something worth playing around with I think.

So anyway, Valentini shows that if there is indeed an equilibrium ensemble of states for the universe then details of particle trajectories cannot be observed and so the pilot wave is essentially unobservable, and hence a non-local HV theory applies which is compatible with QM and the Bell inequalities.

It’s a neat idea.

My bet would be that more conventional spacetime physics which uses non-trivial topology can do a better job of explaining non-locality than the pilot wave. In particular, I suspect requiring a pilot wave to carry all relevant information about all observables is just too much ontological baggage. Like a lot of speculative physics thought up to try to solve foundational problems, I think the pilot wave is a nice explanatory construct, but it is still a construct, and I think something still more fundamental and elementary can be found to yield the same physics without so many ad hoc assumptions.

To relate this with very different ideas, what the de Broglie-Bohm pilot wave reminds me of is the inflaton field postulated in inflationary Big Bang models. I think the inflaton is a fictional construct. Yet it’s predictive power has been very successful. My understanding is that instead of an inflaton field you can use fairly conventional and uncontroversial physics to explain inflationary cosmology, for example the Penrose CCC (Conformal Cyclic Cosmology) idea. This is not popular. But it is conservative physics and requires no new assumptions. As far as I can tell CCC “only” requires a long but finite lifetime for electrons, which should eventually decay by very weak processes. (If I recall correctly, in the Standard Model the electron does not decay.) The Borexino experiment in Italy has measured the lower limit on the electron lifetime as longer than 66,000—yottayears, but currently there is no upper limit.

And for the de Broglie-Bohm pilot wave I think the idea can be replaced by spacetime with non-trivial topology, which again is not very trendy or politically correct physics, but it is conservative and conventional and requires no drastic new assumptions.

What Are the Consequences?

I’m not sure what the consequences of cosmic HV’s are for current physics. The main consequence seems to be an altered understanding of the early universe, but nothing dramatic for our current and future condition. In other words, I do not think there is much use for cosmic HV theory.

Philosophically I think there is some importance, since the truth of cosmic HV’s could fill in a lot of gaps in our civilisations understanding of quantum mechanics. It might not be practically useful, but it would be intellectually very satisfying.

Is Their Any Evidence for these Cosmic HV’s?

According to Valentini, supposing at some time in the early Big Bang there was non-equilibrium, hence classical physics more or less, then there should be classical perturbations frozen in the cosmic microwave radiation background from this period. This is due to a well-known result in astrophysics where perturbations on so-called “super Hubble” length scales tend to be frozen — i.e., they will still exist in the CMB.

Technically what Valentini et al., predict is a low-power anomaly at large angles in the spectrum of the CMB. That’s fine and good, but (contrary to what Valentini might hope) it is not evidence of non-equilibrium quantum mechanics with pilot waves. Why not? Simply because a hell of a lot of other things can account for observed low-power anomalies. Still, it’s not all bad — any such evidence would count as Bayesian inference support for pilot wave theory. Such weak evidence abounds in science, and would not count as a major breakthrough, unfortunately (because who doesn’t enjoy a good breakthrough?) I’m sure researchers like Valentini, in any sciences, in such positions of lacking solid evidence for a theory will admit behind closed doors the desultory status of such evidence, but they do not often advertise it as such.

It seems to me so many things can be “explained” by statistical features in the CMB data. I think a lot of theorist might be conveniently ignoring the uncertainties in the CMB data. You cannot just take this data raw and look for patterns and correlations and then claim they support your pet theory. At a minimum you need to use the uncertainties in the CMB data and allow for the fact that your theory is not truly supported by the CMB when alternatives to your pet theory are also compatible with the CMB.

I cannot prove it, but I suspect a lot of researchers are using the CMB data in this way. That is, they can get the correlations they need to support their favourite theory, but if they include uncertainties then the same data would support no correlations. So you get a null inconclusive result overall. I do not believe in HV theories, but I do sincerely wish Valentini well in his search for hard evidence. Getting good support for non-mainstream theories in physics is damn exciting.

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Epilogue — Why HV? Why not MWI? Why not …

At the same conference Max Texmark polls the audience on their favoured interpretations of QM. The very fact people can conduct such polls among smart people is evidence of areal science of scientific anthropology. It’s interesting, right?! The most popular was Undecided=24. Many Worlds=15. Copenhagen=2. Modified dynamics (GRW)=0. Consistent Histories=0. Bohm (HV)=5. Relational=2. Modal=0.

This made me pretty happy. To me, undecidability is the only respectable position one can take at this present juncture in the history of physics. I do understand of course that many physicists are just voting for their favourites. Hardly any would stake their life on the fact that their view is correct. still, it was heart-warming to see so many taking the sane option seriously.

I will sign off for now by noting a similarity between HV and MWI. There’s not really all that much they have in common. But they both ask us to accept some realities well beyond what conservative standard interpretation-free quantum mechanics begs. What I mean by interpretation-free is just minimalism, which in turn is simply whatever modeling you need to actually do quantum mechanics predictions for experiments, that is the minimal stuff you need to explain or account for in any metaphysics interpretations sitting on top of QM. There is, of course, no such interpretation, which is why I can call it interpretation-free. You just go around supposing (or actually not “supposing” but merely “admitting the possibility”) the universe IS this Hilbert space and that our reality IS a cloud of vectors in this space that periodically expands and contracts in consistency with observed measurement data and unitary evolution, so that it all hangs together consistently and a consistent story can be told about the evolution of vectors in this state space that we take as representing our (possibly shared) reality (no need for solipsism).

I will say one nice thing about MWI: it is a clean theory! It requires a hell of a lot more ontology, but in some sense nothing new is added either. The writer who most convinces me I could believe in MWI is David Deutsch. Perhaps logically his ideas are the most coherent. But what holds me back and forces me to be continually agnostic for now (and yes, interpretations of QM debates are a bit quasi-religious, in the bad meaning of religious, not the good) is that I still think people simply have not explored enough normal physics to be able to unequivocally rule out a very ordinary explanation for quantum logic in our universe.

I guess there is something about being human that desires an interpretation more than this minimalism. I am certainly prey to this desire. But I cannot force myself to swallow either HV(Bohm) or MWI. They ask me to accept more ontology than I am prepared to admit into my mind space for now. I do prefer to seek a minimalist leaning theory, but not wholly interpretation-free. Not for the sake of minimalism, but because I think there is some beauty in minimalism akin to the mathematical idea of a Proof from the Book.